### Malliavin differentiability of the Heston volatility and applications to option pricing

Elisa Alòs and Christian-Oliver Ewald
Source: Adv. in Appl. Probab. Volume 40, Number 1 (2008), 144-162.

#### Abstract

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

First Page:
Primary Subjects: 91B28
Secondary Subjects: 60H07, 60H10, 60H30
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1208358890
Digital Object Identifier: doi:10.1239/aap/1208358890
Mathematical Reviews number (MathSciNet): MR2411818
Zentralblatt MATH identifier: 1137.91422

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